If the original contract does not contain any terms that would prohibit you from assigning responsibilities to another party, then you don’t have to. However, some may consider it common courtesy to alert them that someone else or another company will be fulfilling the contract.
It is a good idea to include clauses about the governing law, indemnification, and future amendments. Moreover, the Agreement Assignment should contain the compensation and the extent of the assignment (a full or partial assignment of the contract).
Notarization is not required. But if you suspect that something might go wrong, getting it notarized can make the signatures harder to challenge in court in the future.
When you assign a contractual agreement to another party, you are assigning the whole shebang. On the other hand, delegation only transfers the responsibilities without the contractual rights. Think of it this way – after you signed a contractual agreement to renovate a house, you can go ahead and delegate some of the work to an electrician, a plumber, and other specialists, for whom you will create a separate contract. This is as opposed to you assigning part or all of the contract to another party.
If the original contract specifically forbids the assignment of obligations, you should not try to use an Agreement Assignment and get someone else to do the work. That is if you do not want to end up in a dispute. What you can do is try to get permission first.